Final answer:
The New York colonists struggled with the lack of a representative assembly until 1683 due to the Duke of York's disinterest in local governance; this situation changed with Governor Thomas Dongan's instructed establishment of a colonial assembly.
Step-by-step explanation:
It took the New York colonists nearly 20 years to establish a legislature because the Duke of York, who controlled the colony, had no desire to govern locally or heed the colonists' wishes for self-representation and a say in matters like taxation. The situation persisted until the appointment of Governor Thomas Dongan in 1683, who was instructed by the Duke to establish a colonial assembly. Despite initially approving the 'Charter of Liberties and Privileges', which outlined the colonists' rights, the subsequent English king, James II, reversed his stance, leading to tension and the eventual inclusion of New York in the Dominion of New England. This decision exacerbated political unrest and set the stage for a revolt against the increasing arbitrary rule and among other events, led to continued struggles for a balance of power between governors and local assemblies.